Physics unit 6

A narrow tube contains air and has one open end and one end closed by a movable piston. At fixed sound frequency f, resonance occurs at physical air-column lengths L = 15, 49 and 83 cm. An end correction e makes the effective length Leff = L+e. For this tube the allowed resonances obey L+e = (2n−1)λ/4, n = 1, 2, 3, ... , where wavelength λ and sound speed c satisfy c = fλ. Assume the three observed resonances are consecutive, that e is independent of n, and that 0 < e < 5 cm. In a second experiment the frequency is doubled with unchanged c and e. Ignore damping shifts.